I think I´ve found evidence that it is indeed Picket Pin in the pictures with William F. Cody.
He is mentioned in the following newspaper article of 1902 as been wounded by an unbroken new horse.
That is why he appears in the photographs with a bandaged arm.
In a second newspaper, another picture taken on the same occasion was printed in 1902.
WITH THE WILD WEST SHOW
BREAKING IN NEW HORSES BY REASON
OF THE NUMBER KILLED IN RAIL-
ROAD ACCIDENT-SCENES IN
TRAINING ARENA.
"Whoa! Whoa! Look out there! Ugh-d**n!"
and as Picket Pin, sub-chief of the Buffalo Bill
Indians, crawled to his feet with a badly dislocated
arm and shook the dust from his gigantic
frame, a wiry little Western horse went scudding
around the canvas walled arena at breakneck speed.
It was on the training grounds of the big Wild
West Show, just out of Bridgeport, Conn., and
Picket Pin is not the only man who has bitten
the dust in that hoof ploughed arena within the
last few days.
With the opening in Madison Square Garden
coming to-morrow and nearly two hundred un-
broken horses to train, there have been, as “Major
John M. Burke, the press agent of the show, put it,
"things doing" in Bridgeport for the last few days.
And Colonel W. F. Cody, standing near, added
that people would certainly get their moneys
worth in "wildness" and "wooliness" who attended
the opening performances. The Tribune man, as
he crawled under a ring rope just in time to miss
a hoof print in the middle of his back, came to the
mental conclusion that they knew whereof they
spoke. […]
New-York tribune., April 20, 1902, Page 12
photo printed in Deseret Evening News August 13, 1902
"Buffalo Bill" & Picket Pin